Man, I had the exact problem you're describing.
I'd made a few "single state" games such as Snake and Pong, but as soon as I tried to put my own together, I was immediately stumped, because I didn't know how to move through the various game states, ie:
Splash screen -> Main menu -> Game (etc)
will explain everything you need to know about states and how to manage them. it may look complex at first but it's actually quite simple. You have a base state class that all states inherit, and a state manager class that deals with switching between them. That way, each state of the game is split into its own class, with it's own game loop. Lovely stuff.
Btw, unless you have a lot of experience with SDL and C++, I recommend following a few of the earlier tutorials before that one, as you might find it hard to pick up. Having said that, it should be fairly straightforward to understand.